On the eigenvalues of specially low-rank perturbed matrices (Q555470)

In recent years much attention has been devoted to the second eigenvalue problem of a Google matrix, which is critical for the convergence rate of the power-related methods used for Google's PageRank computation. A Google matrix can be considered as a special case of a matrix \(A\) perturbed by a low-rank matrix \(U\) consisting of a number of linearly independent eigenvectors of \(A\). The author allows \(U\) to consist of a basis of an invariant subspace of \(A\) and also considers cases where \(U\) does not have full col-rank. Earlier results are found to transform into similar results for the generalized \(U\). Applications to a few interesting problems are presented.